Question

In an isosceles triangle ABC, AB=AC and BC is produced to D. Prove that

AD² - AC² = BD ×CD

Answer 1

GiveTriangle ABC with AB=AC,BC produced to point D.

To Prove：AD>AB

Figure would be like this

Proof：Since in triangle ABC,AB=AC

Therefore, angle ABC=Angle ACB（angles opposite to equal sides of a triangle……（1）

In triangle ACD,since angle ACB is an exterior angle

angle ACB>angle ADC（exterior angle of a triangle is greater than each interior opposite angles.）

now,angle ABC>Angle ADC….….from（1）

In triangle ABD,


since angle ABC > angle ADC

AD>AB （side opposite to greater angle is larger）

hence proved